Chapter 3, Polynomial and Rational Functions - Section 3.5 - Complex Zeros and the Fundamental Theorem of Algebra - 3.5 Exercises - Page 329: 19

The completely factored form of P(x) is: $P(x)=(x-5i)(x+5i)$ The zeros of the function are: $\{5i,-5i\}$ x = –5i with multiplicity 1 x = 5i with multiplicity 1

Factor the polynomial completely to obtain: $P(x)=x^{2}+25$ $P(x)=(x-5i)(x+5i)$ Equate each unique factor to zero then solve each equation to obtain: $x-5i=0 \rightarrow x=5i$ $x+5i=0 \rightarrow x=-5i$ The zeros of the function are: $\{5i,-5i\}$ x = –5i with multiplicity 1 x = 5i with multiplicity 1